A Study of Psi-Function

Authors

  • Y. Pragathi Kumar Department of Mathematics, College of Natural and Computational Sciences, Adigrat University, Adigrat
  • B. Satyanarayana Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar 522510, Andhra Pradesh

DOI:

https://doi.org/10.26713/jims.v12i2.1340

Keywords:

\(I\)-function, \(H\)-function, Mellin transform, Laplace transform, General class of polynomials, Struve's function

Abstract

The aim of this paper is to introduce a new generalization of the well-known, interesting and useful Fox \(H\)-function and \(I\)-function into generalized function, namely, the Psi-function. From which authors obtained I-function defined by Saxena [17] and Rathie [8]. Convergent conditions, elementary properties, and special cases have also been given.

Downloads

Download data is not yet available.

References

T. W. Anderson, An Introduction to Multi Variable Statistical Analysis, John Wiley, New York (1984), http://www.ru.ac.bd/stat/wp-content/uploads/sites/25/2019/03/301_03_Anderson_An-Introduction-to-Multivariate-Statistical-Analysis-2003.pdf.

A. Erdelyi, Table of Integral Transforms, Vol. I, McGraw-Hill Book Co., New York (1953). [3] C. Fox, The G and H-functions as symmetrical Fourier kernels, Transactions of American Mathematical Society 98, 196 (1961), 395 – 429.

I. S. Gradshteyin and I. M. Ryzhik, Table of Integrals, Series and Products, 6/e, Academic Press, New Delhi (2001).

J. Mishra and N. Pandey, An integral involving general class of polynomials with I-function, International Journal of Scientific and Research Publications 3(1) (2013), 1 – 3, http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.299.3408&rep=rep1&type=pdf.

Y. L. Luke, The Special Functions and Their Approximations, Vol. 1, Academic Press, New York (1969), https://ia601608.us.archive.org/0/items/in.ernet.dli.2015.141299/2015.141299.The-Special-Functions-And-Their-Approximations-Vol-1.pdf.

M. Garg and S. Mittal, On a new unified integral, Proceedings of the Indian Academy of Sciences - Mathematical Sciences 114(2) (2004), 99 – 101, DOI: 10.1007/BF02829845.

A. K. Rathie, A new generalization of generalized hypergeometric functions, Le Mathematiche, I, LII Fasc. II (1997), 297 – 310, https://arxiv.org/ftp/arxiv/papers/1206/1206.0350.pdf.

B. Satyanarayana and Y. P. Kumar, Integral transform involving the product of general class of polynomials, Struve's function, H-function of one variable and H-function of ‘r' variables, Applied Mathematical Sciences 5(57) (2011), 2831 – 2838, http://www.m-hikari.com/ams/ams-2011/ams-57-60-2011/pragathiAMS57-60-2011.pdf.

B. Satyanarayana, P. Y. Kumar, N. Srimannarayana and B. V. Purnima, Solution of boundary value problems involving I-function and Struve's function, International Journal of Recent Technology and Engineering 8(3) (2019), 411 – 415, https://www.ijrte.org/wp-content/uploads/papers/v8i3/C4205098319.pdf.

B. Satyanarayana, P. Y. Kumar and B. V. Purnima, Mellin and Laplace transforms involving product of Struve's function and I-function of two variables, Arya Bhatta Journal of Mathematics and Informatics 10(1) (2018), 17 – 24, https://2164ee62-242c-4927-ad0ce25decce551c.filesusr.com/ugd/1ee7d3_24062fd20dbd485c9922cf89322f9178.pdf.

P. Jain, A. Gupta and V. P. Saxena, Multiple integral involving I-function and Bessel-Maitland functions, International Journal of Mathematics Trends and Technology 39(3) (2016), 232 – 237, https://ijmttjournal.org/2016/Volume-39/number-3/IJMTT-V39P529.pdf.

Y. P. Kumar, A. Mabrahtu, B. V. Purnima and B. Satyanarayan, Mellin and Laplace transforms involving the product of extended general class of polynomials and I-function of two variables, International Journal of Mathematical Sciences and Engineering Applications. 10(III) (2016), 143 – 150, http://www.ascent-journals.com/IJMSEA/Vol10No3/13-kumar.pdf.

Y. P. Kumar, L. P. Rao and B. Satyanarayana, Derivatives involving I-function of two variables and general class of polynomials, British Journal of Mathematics and Computer Science 9(5) (2015), 446 – 452, https://doi.org/10.9734/BJMCS/2015/17700.

Y. P. Kumar and B. Satyanarayana, Integral transform involving the product of general class of polynomials and H-function of two variables, Arya Bhatta Journal of Mathematics and Informatics 3(1) (2011), 43 – 48.

V. P. Saxena, A formal solution of certain new pair of dual integral equations involving H-functions, Proceedings of the National Academics of Science, India 52(A) III (1982), p. 336 – 375.

V. P. Saxena, The I-function, Anamaya Publishers, New Delhi (2008).

H. M. Srivastava, K. C. Gupta and S. P. Goyal, The H-functions of One and Two Variables with Applications, South Asian Publishers, New Delhi (1982).

V. Jat, V. P. Saxena and P. L. Sanodia, On certain special cases of existence conditions of I-function, Jnanabha 48(1) (2018), 72 – 78, http://docs.vijnanaparishadofindia.org/jnanabha/jananabha_volume_48_v1_2018/jnanabha_volume_48_v1_2018.pdf.

Downloads

Published

2020-06-30
CITATION

How to Cite

Kumar, Y. P., & Satyanarayana, B. (2020). A Study of Psi-Function. Journal of Informatics and Mathematical Sciences, 12(2), 159–171. https://doi.org/10.26713/jims.v12i2.1340

Issue

Vol. 12 No. 2 (2020)

Section

Research Articles

License

Authors who publish with this journal agree to the following terms:
  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.